Time and Work
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Q.

To complete a piece of work $A$ and $B$ take 8 days, $B$ and $C$ 12 days. $A$, $B$ and $C$ take 6 days. $A$ and $C$ will take :

 A.

7 Days

 B.

7.5 Days

 C.

8 Days

 D.

8.5 Days

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Solution:
Option(C) is correct

Given $(A+B)$'s  one day’s work = \(\dfrac{1}{8}\)

$(B+C)$'s  one day’s work = \(\dfrac{1}{12}\)

$(A+B+C) $'s 1 day’s work = \(\dfrac{1}{6}\)

Work done by $A$, alone:

$=(A+B+C)$'s 1 day’s work - $(B+C)$'s  one day’s work

$= \dfrac{1}{6} - \dfrac{1}{12}$

$=\dfrac{1}{12}$

Work done by $C$, alone:

$=(A+B+C) $'s 1 day’s work - $(A+B)$'s  one day’s work

$= \dfrac{1}{6} - \dfrac{1}{8}$

$=\dfrac{1}{24}$

$(A+C)$'s one day’s work:

$=\dfrac{1}{12}+\dfrac{1}{24}$ 

$=\dfrac{1}{8}$

$(A+C)$ will take $\textbf{8 days}$ to complete the work together.

Edit:For an alternative solution, check comment by Manpreet Kunnath.


(9) Comment(s)


ABHI
 ()

A+B = 1/8th of the work

B+C = 1/12th of the work

A+B+C = 1/6th of the work

C= 1/6-1/8 =1/24

A= 1/6- 1/12 = 1/12

C+A = 1/24+ 1/12 = 3/24 i.e., 1/8th of the work

So togather they will take 8days

Hope you guys know the basics



Pavan Kumar
 ()

Given (1/A+1/B)=1/8

(1/B+1/C)=1/12

(1/A+1/B+1/C)=1/6 Then

2* (1/A+1/B+1/C)=2/6 => (1/A+1/C)=2/6-1/8-1/12 =>

After solving above one we will get

(1/A+1/C)=1/8

so 8 days required to complete the work if A and C are worked to gether


Anvesh
 ()

How 1/A can be work done in one day ? Pls do reply


Manpreet Kunnath
 ()

$A+B+C=6$ ..... (1)

$A+B=8$ ..... (2)

Replacing (2) in (1)

$8+C=6$

Hence, $C=2$ (Ignoring the negative symbol)

$B+C=12$ ..... (3)

replacing (3) in (1)

$A+12=6$

Hence, $A=6$ (Ignoring the negative symbol)

So adding the two results

$A+C = 6+2$

$= \textbf{8 days}$



Suhail Ahmed
 ()

We have formula for this:

$=\dfrac{2XYZ}{XY+YZ+ZX}$

Simply solve for $=ZX$



S Malik
 ()

@Shireen like $A+B=8$ SO $A=8-B$ and so on


Shireen
 ()

Tried but could not work out the calculation, any help please.


Muhammad Shehroz
 ()

Keep it simple. Put values of $A+B$ and $B+C$ in $A+B+C=6$ equation to get values of $C$ and $A$ simultaneously.


Shireen
 ()

Can you please elaborate more?